You hit the nail on the head. I was trying to understand Rick James's position, and it occurred to me that if you thought of parents as having the right to total and complete control over everything about their child (as some conservatives do) - what we're calling ownership - then the thought of transferring that right to the state is indeed pretty disgusting.

Commenters are articulating this pretty well, though. Children have their own rights, and the state enforces them. Even a "ward of the state" is not owned by the state, the state is just the entity which is currently responsible for meeting his needs.